Well you definitely know more than me about this subject so I won't quarrel. Most people outside California do speak about the same as Californians as far as I can discern.
Let's start with this: do you pronounce the words "cot" and "caught" differently? "Don" and "Dawn"? "The fawns" and "The Fonz"? (I think you might.) If so, then, no, you don't talk like a Californian
I've lived in California my entire life & I have never heard anyone pronounce those the same. "Cot", "Don", & "Fonz" have a vowel sound like the "a" in "father". "Caught", "dawn", & "fawns" sound like the "aw" in "paw".
Ah! I was wondering why. Then I saw you were from San Francisco. Yes, you might. Angelenos would consider you saying such a thing bizarre.
This is strange to me. I know that at one point San Francisco had an accent very different from California English and rather like the Boston accent, but I thought that only old people used that now. I've never heard anyone without the cot-caught merger and I don't even understand how one would pronounce cot and caught differently. That said, I don't actually know anyone from San Francisco.
I don't either, so... *shrug*. Might just be the result of constant in-migration from elsewhere (think the tech boom in the 90s).
How do you know you haven't heard anyone without the cot-caught merger, by the way? Part of the merger is that you can't perceive the difference between the two, so theoretically if you have ever come into contact with someone without the merger you just wouldn't've noticed that they were producing reliable differences between the vowels
see pronouncing "caught" & "cot" the same if one were to speak very rapidly, since the "ah" sound is easier to form than the "aw" sound & just tends to come out naturally for me if I speak about as fast as a Parisian would. Even then, it still typically falls somewhere between "ah" & "aw". I'm pretty sure that American English isn't spoken like that, though, so maybe something else is at work.